Simplex sliding mode methods for the chattering reduction control of multi-input nonlinear uncertain systems

The simplex sliding mode control method is further developed by considering uncertain control systems non-affine in the control law. In order to reduce chattering effects, a set of integrators is added in the input channels. The augmented system is then controlled by a switching logic based on the simplex control method. As a result, the original control vector turns out to be continuous. A second order sliding mode observer is used when the sliding output is not available. Explicit conditions are identified about systems uncertainties and the simplex geometry in order to guarantee the convergence of the proposed methodology.